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4x-3(5x+8)<_-7 inequation

A inequation with variable

The solution

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4*x - 3*(5*x + 8) <= -7
$$4 x - 3 \left(5 x + 8\right) \leq -7$$
4*x - 3*(5*x + 8) <= -7
Detail solution
Given the inequality:
$$4 x - 3 \left(5 x + 8\right) \leq -7$$
To solve this inequality, we must first solve the corresponding equation:
$$4 x - 3 \left(5 x + 8\right) = -7$$
Solve:
Given the linear equation:
4*x-3*(5*x+8) = -7

Expand brackets in the left part
4*x-3*5*x-3*8 = -7

Looking for similar summands in the left part:
-24 - 11*x = -7

Move free summands (without x)
from left part to right part, we given:
$$- 11 x = 17$$
Divide both parts of the equation by -11
x = 17 / (-11)

$$x_{1} = - \frac{17}{11}$$
$$x_{1} = - \frac{17}{11}$$
This roots
$$x_{1} = - \frac{17}{11}$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} \leq x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{17}{11} + - \frac{1}{10}$$
=
$$- \frac{181}{110}$$
substitute to the expression
$$4 x - 3 \left(5 x + 8\right) \leq -7$$
$$\frac{\left(-181\right) 4}{110} - 3 \left(\frac{\left(-181\right) 5}{110} + 8\right) \leq -7$$
-59       
---- <= -7
 10       

but
-59       
---- >= -7
 10       

Then
$$x \leq - \frac{17}{11}$$
no execute
the solution of our inequality is:
$$x \geq - \frac{17}{11}$$
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Solving inequality on a graph
Rapid solution [src]
   /-17              \
And|---- <= x, x < oo|
   \ 11              /
$$- \frac{17}{11} \leq x \wedge x < \infty$$
(-17/11 <= x)∧(x < oo)
Rapid solution 2 [src]
 -17      
[----, oo)
  11      
$$x\ in\ \left[- \frac{17}{11}, \infty\right)$$
x in Interval(-17/11, oo)